Question

I saw that in the column on AI, the Rabbi says that a rabbi has no authority to permit or prohibit.
Why then do we find, regarding a clearly established rabbi, "after Rabbi Eliezer to Lod"?
And what is the meaning of, "If he acted according to the words of Beit Shammai, he acted; according to the words of Beit Hillel, he acted"?
There it is talking about an ordinary person who decides whom to follow in his halakhic ruling, even though he is not a student of any specific rabbi.
And really, how does a person choose his rabbi for this purpose, if such a thing exists at all?